A remark on the Sobolev regularity of classical solutions to uniformly parabolic equations

Journal article

Authors/Editors

Milani, Albert

Research Areas

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Publication Details

Author list: Milani A

Publisher: WILEY-V C H VERLAG GMBH

Place: BERLIN

Publication year: 1999

Journal acronym: MATH NACHR

Volume number: 199

Start page: 115

End page: 144

Number of pages: 30

ISSN: 0025-584X

Languages: English-Great Britain (EN-GB)

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Abstract

We prove that C-2+alpha,C- 1+alpha/2((Q) over bar) solutions of problem (1.6) below are in a subspace H-c(m+2)(Q) of H-m+2,H-(m+2/2)(Q) for all m is an element of N, if f and the coefficients are in H-c(m)(Q)boolean AND C-alpha,C-alpha/2((Q) over bar). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below.

Keywords

parabolic equations, regularity

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